Easy
If $P$,$Q$,and $R$ are three points on a line,and $Q$ lies between $P$ and $R$ [see figure],then prove that $PQ + QR = PR$.
(N/A) In the figure given above,the line segment $PR$ coincides with the sum of line segments $PQ$ and $QR$.
Euclid's axiom $(4)$ states that things which coincide with one another are equal to one another.
Therefore,it can be deduced that $PQ + QR = PR$.
Note that,in this solution,it has been assumed that there is a unique line passing through two distinct points.
Euclid's axiom $(4)$ states that things which coincide with one another are equal to one another.
Therefore,it can be deduced that $PQ + QR = PR$.
Note that,in this solution,it has been assumed that there is a unique line passing through two distinct points.
Explore More
Similar Questions
The number of dimensions a point has is:
Easy
View SolutionRam and Ravi have the same weight. If they each gain weight by $2\, kg$,how will their new weights be compared?
Easy
View SolutionSolve the following question using an appropriate Euclid's axiom:
In the figure:
$AB = BC$,$M$ is the mid-point of $AB$ and $N$ is the mid-point of $BC$. Show that $AM = NC$.
In the figure:
$AB = BC$,$M$ is the mid-point of $AB$ and $N$ is the mid-point of $BC$. Show that $AM = NC$.
Medium
View SolutionEuclid divided his famous treatise 'The Elements' into $\ldots \ldots \ldots$ chapters.
Easy
View SolutionOne dimension in each step in the sequence of solids $-$ surfaces $-$ lines $-$ points is........ going on.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo